Prof. Maier's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT
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Speaker:
Matthias Maier, University of Heidelberg

Title:
Model adaptation in context of multiscale methods

Abstract:
  A large class of modeling problems in Physics and Engineering is of
  multiscale character, meaning, that relevant physical processes act on
  highly different length scales. This usually implies high computational
  cost for a full resolution of the problem. One way to avoid such a full
  resolution are multiscale schemes, where, generally speaking, an effective
  model is solved on a coarse scale with upscaled, effective parameters.
  Those paramaters are determined with the help of localized sampling
  problems on a fine scale.

  Multiscale schemes introduce significant complexity with respect to
  sources of error, not only are there discretization errors on a coarse
  and fine scale, but also a model error introduced by the modeling
  assumption. This makes suitable a posteriori strategies highly
  necessary.

  In this talk different model adaptation strategies for the Variational
  Multiscale Method (VMM) and the Heterogeneous Multiscale Method (HMM)
  are examined and a general framework for model adaptation (based on the
  HMM) is introduced. The framework is derived within the setting of
  ``goal-oriented'' adaptivity given by the so-called Dual Weighted
  Residual (DWR) method.
  Based on the framework a sampling-adaptation strategy is proposed that
  allows for simultaneous control of discretization and model errors
  with the help of classical refinement strategies for mesh and sampling
  regions. Further, a model-adaptation approach is derived that
  interprets model adaptivity as a minimization problem of a local
  model-error indicator.

Venue: Wednesday 1 April at 2 pm in SISSA lecture room 005